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Applying the chain rule using trees?

  1. Apr 29, 2013 #1
    1. The problem statement, all variables and given/known data
    Write out a tree (this will be a big tree) of dependencies and hence write down an expression for
    ∂z/∂r


    2. Relevant equations
    z=k(x, y)=xy2, x=(w1)(w2)+w3, y=w4;

    w1=t, w2=t2, w3=2t+1, w4=sin(t);
    t=r2+2s2


    3. The attempt at a solution
    This is the tree I drew and followed the relevant paths in order to try and write and expression but my expression is to short. I only calculate 2 terms when there is suppose to be 8:
    http://www.picpaste.com/Untitled_Image-OZCiTMvb.jpg [Broken]

    This is wrong however. I need 16 leaves at the base. What am I doing wrong?
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Apr 29, 2013 #2

    Mark44

    Staff: Mentor

    I drew a diagram and got the same one you did.

    As far as your partial ## \partial z/\partial r## is concerned, I get four terms to your two. Three of the four terms look like this:
    $$ \frac{\partial z}{\partial x} \frac{\partial x}{\partial w_i} \frac{d w_i}{dt} \frac{\partial t}{\partial r}$$

    For the fourth one, the first factor is the partial of z with respect to y.
     
    Last edited by a moderator: May 6, 2017
  4. Apr 29, 2013 #3

    SammyS

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    attachment.php?attachmentid=58345&stc=1&d=1367266069.jpg
     

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